Question

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

logarithmic graph passing through point 1, negative 2.

f(x − 2)
f(x + 2)
f(x) − 2
f(x) + 2

Answer 1

Answer: Third option

`f(x) - 2`

Explanation:

The function
`y=log_3 (x)` passes through the point (1,0) since the function
`y=log_a (x)` always cuts the x-axis at
`x = 1`.

Then, if the transformed function passes through point (1,-2) then this means that the graph of
`y=log_3(x)` was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

`y = f (x) + k`

Where k is a negative number. In this case
`k = -2`

Then the transformation is:

`f(x) -2`

and the transformed function is:

`y = log_3 (x) -2`